I set this up after my first child was born so that my wife and I, along with all of the other family members could post pictures and videos of our daughter (and our family) on a machine I control. When someone babysits her and takes pictures/videos they too can post them.

This serves us in many ways. For instance, we have all of the pictures in one place, not spread over many services depending on where family members post them -- although some family members also post to facebook :( For the grandmothers and grandfathers we just give them the url instead of trying to explain a YouTube channel to them. They know how urls work, not how YouTube works.

This also serves as a backup. The server is hosted outside our apartment so the pictures we put there can be easily fetched in case something happens to our apartment (and computers - but this can also be fixed with a backup server, this is a side effect).

Basically, family album in one place -- no matter who the photographer is (and backup).